Verify the equation: n(A∪B)=n(A)+n(B) For the given disjoint set A={a,e,i,o,u} and B={g,h,k,l,m}

Thus, there are approximately 408 students who are taking an online course and prefer basketball to football.

To solve this problem, we need to use the formula for the intersection of two independent events:

P(A and B) = P(A) * P(B)

where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A and B) is the probability of both events A and B occurring simultaneously.

In this case, let A be the event of taking an online class, and let B be the event of preferring basketball to football. We are asked to find the number of students who are in the intersection of these two events, or P(A and B).

We are given that there are 1200 students taking an online class, out of a total of 5000 students. Therefore, the probability of taking an online class is:

P(A) = 1200/5000 = 0.24

We are also given that 1700 students prefer basketball to football. Since this event is independent of taking an online class, the probability of preferring basketball to football is simply:

P(B) = 1700/5000 = 0.34

Now we can use the formula to find the probability of both events occurring simultaneously:

P(A and B) = P(A) * P(B) = 0.24 * 0.34 = 0.0816

Finally, we can convert this probability to a number of students by multiplying by the total number of students:

0.0816 * 5000 = 408

Therefore, there are approximately 408 students who are taking an online course and prefer basketball to football.

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The order approximately 1.1111 cubic yards of topsoil from the dirt store.

The volume of topsoil required in cubic feet.

The area of the garden is:

The area of the garden is found by multiplying the length and width of the garden. In this case, the garden is 15 feet by 12 feet, so the area is 15 ft x 12 ft = 180 sq ft.

Since we want a 2 inch thick layer of topsoil, we need to convert the thickness to feet:

2 inches = 2/12 feet = 0.1667 feet

The volume of topsoil required in cubic feet is therefore:

180 sq ft × 0.1667 ft = 30 cubic feet

To convert this to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):

The dirt store sells topsoil by the cubic yard, so we need to convert our answer from cubic feet to cubic yards. Since there are 27 cubic feet in a cubic yard (3 feet x 3 feet x 3 feet)

30 cubic feet ÷ 27 = 1.1111 cubic yards

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To find the measure of angle BOC, set the expressions for m∠AOD and m∠BOC equal and solve for x. Then substitute the value of x back into the expression for m∠BOC to find its measure, which is 30°.

To find the measure of angle BOC, we can set the expressions for m∠AOD and m∠BOC equal to each other and solve for x.

7x - 5 = 3x + 15

Subtract 3x from both sides: 4x - 5 = 15

Add 5 to both sides: 4x = 20

Divide both sides by 4: x = 5

Now that we know x = 5, we can substitute it back into the expression for m∠BOC to find its measure.

m∠BOC = (3x + 15)° = (3*5 + 15)° = 30°

Therefore, the measure of ∠BOC is 30°, which corresponds to option B.

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The value of x if the angles are congruent angles is 4

From the question, we have the following parameters that can be used in our computation:

(5x+2)° (4x+6)°

Assuming the angles are congruent angles

Then we have

(5x+2)° = (4x+6)°

Remove the bracket and the degree sign

So, we have

5x + 2 = 4x + 6

When the like terms are evaluated, we have

x = 4

This means that the value of x is 4

Note that the condition is that the angles (5x+2)° and (4x+6)° are congruent angles

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The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

(6/2x) + (4/2x) = 1/4

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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The model's rigging length of 326 feet is likely only a fraction of the total rigging on the real Lady Washington. Nonetheless, it is still an astonishing amount of string to work with when creating a model ship!

Assuming that the scale model is an accurate representation of the Lady Washington, we can use the model's rigging length to estimate the total rigging of the actual ship. The model has 326 feet of rigging, and if we know the scale of the model, we can determine the length of the real ship's rigging.
Unfortunately, without knowing the scale of the model or the dimensions of the actual ship, it is impossible to give an exact answer. However, we can make some educated guesses based on typical rigging lengths for ships of a similar size and type.
The Lady Washington is a replica of an 18th-century trading vessel, and based on historical records, we can estimate that a ship of this type and size would have had around 1,000 feet of rigging. This includes the standing rigging (which supports the mast and stays in place all the time), as well as the running rigging (which is used to adjust the sails).

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The rate of decay, denoted as 'r,' is a key factor in exponential functions, particularly when modeling real-world scenarios such as population decrease, radioactive decay, and depreciation of assets.

In an exponential decay function, the form is y = ab^(rt), where 'y' represents the remaining quantity, 'a' is the initial quantity, 'b' is the base, 'r' is the rate of decay expressed as a decimal, and 't' is the time elapsed.

The rate of decay, r, is a constant value that determines how rapidly the quantity decreases over time. It is expressed as a decimal (e.g., 0.2 for a 20% decay rate) and should be between 0 and 1 for decay scenarios. When determining the rate of decay, it is essential to gather data points that can be plotted on a graph to create an exponential curve, allowing you to estimate the decay rate accurately.

In some cases, the exponential decay equation can be written as y = ae^(-rt), where 'e' is the base of natural logarithms, approximately equal to 2.718. This is another representation of the same decay process and follows the same principles in terms of decay rate calculations.

To find the rate of decay for a specific dataset, you can use various techniques, including curve fitting or regression analysis, which help to find the best match between the data points and the exponential decay function.

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Based on the 2012 Gallup survey that interviewed a random sample of 474,195 U.S. adults, it can be reasonably concluded that there is a slightly higher prevalence of obesity among unemployed individuals who are actively seeking work (28.6%) compared to those who are employed (24.9%).

However, it is important to note that this survey only provides a snapshot of a specific time period and may not be representative of the entire U.S. population. Additionally, other factors such as age, gender, and socio-economic status may also influence obesity rates and were not accounted for in this survey.

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If 400 hypothesis tests are conducted with a null hypothesis assumed to be true and using a significance level of 1%, approximately 4 tests will incorrectly find significance. This is because 1% of 400 is 4 (0.01 x 400 = 4).

If the null hypothesis is true, then we would expect approximately 1% of the tests to result in a Type I error, which is incorrectly rejecting the null hypothesis. Therefore, out of the 400 tests conducted at a significance level of 1%, we would expect approximately 4 tests to incorrectly find significance.

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For the data generated by the questionnaire item that asked students to indicate their class rank in college, the appropriate measure of location would be the mode.

The mode is the value that occurs most frequently in a dataset and represents the most common response. In this case, the mode would indicate the most common class rank among the students surveyed. It is important to note that the use of the mode as a measure of location is most appropriate when dealing with nominal or ordinal data, such as class rank, where there is no inherent numerical relationship between the categories.

Other measures of location, such as the mean or median, are more appropriate for interval or ratio data where there is a meaningful numerical relationship between the values.

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360[/tex]

so since a quadrilateral will have a total of 360°, minus 240 and 20 that leaves us with only 100° leftover, now to make it in a 3 : 7 ratio, let's simply divide 100 by (3 + 7) and distribute accordingly.

[tex]3~~ : ~~7\implies 3\cdot \frac{100}{3+7}~~ : ~~7\cdot \frac{100}{3+7}\implies 3\cdot 10~~ : ~~7\cdot 10\implies 30^o~~ : ~~70^o[/tex]

The value of c depends on the initial conditions x0 and y0. For example, if we are given x0 = 1 and y0 = 2, then c = 1. If we are given x0 = 2 and y0 = 5, then c = 8/3. To solve this problem, we first need to find the derivative of y with respect to x. Using the quotient rule, we get:

y' = (2x^(-3))(cx^4 - 2)

Next, we substitute y and y' into the differential equation and simplify:

xy' + 2y = 4x^2
x(2x^(-3))(cx^4 - 2) + 2(x^2 + c/x^2) = 4x^2
2cx - 2x^(-2) + 2x^2 + 2c/x^2 = 4x^2
2cx + 2c/x^2 = 6x^2
2c(x^3 + 1) = 6x^4
c = 3x/(x^3 + 1)

To satisfy the initial condition, we need to find the value of c that makes y(x) equal to some given value y0 when x = x0. Plugging in x0 and y0 into the equation for y, we get:

y0 = x0^2 + c/x0^2
c = x0^2(y0 - x0^2/x0^2)

In summary, the value of c that satisfies the given differential equation and initial condition depends on the specific values of x0 and y0. We can find c by plugging in these values into the equation for y and solving for c.

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The calculated value of the unit rate of the turkey is $7.2 per pound

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Unit rate = Cost/Pounds of turkey

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 9/(1 1/4)

Evaluate

Unit rate = 7.2

Hence, the unit rate is 7.2

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The Shavers Fork watershed is impacted by acid precipitation or other forms of pollution that are affecting the pH levels of the tributary water basin in the springtime.The data of Exercise 17.8 do give good reason to think that the springtime water in the tributary water basin around the Shavers Fork watershed is not neutral. Here's why:

Step 1: State the null hypothesis and the alternative hypothesis.

Null hypothesis: The springtime water in the tributary water basin around the Shavers Fork watershed is neutral (pH 7.0).

Alternative hypothesis: The springtime water in the tributary water basin around the Shavers Fork watershed is not neutral (pH ≠ 7.0).

Step 2: Determine the appropriate test statistic and the level of significance.

In this case, we can use a t-test for a single sample since we are comparing the pH of the springtime water in the tributary water basin to a neutral pH of 7.0. The level of significance is not given in Exercise 17.8, so we will assume it to be 0.05.

Step 3: Calculate the test statistic and the p-value.

Using the data from Exercise 17.8, we find that the sample mean pH is 6.45 and the sample standard deviation is 0.23. The test statistic is calculated as:

t = (6.45 - 7.0) / (0.23 / sqrt(9)) = -9.78

Using a t-table with 8 degrees of freedom (n-1), we find that the p-value is less than 0.001.

Step 4: Make a decision and interpret the results.

Since the p-value is less than the level of significance of 0.05, we reject the null hypothesis and conclude that the springtime water in the tributary water basin around the Shavers Fork watershed is not neutral. The data suggest that the pH of the water is significantly lower than a neutral pH of 7.0, indicating that the water is acidic. Therefore, we can infer that the Shavers Fork watershed is impacted by acid precipitation or other forms of pollution that are affecting the pH levels of the tributary water basin in the springtime.

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If the sand falls at a rate of 16 cubic millimeters per second, a player would have approximately 6.25 seconds for their turn.

The rate of sand falling from the hourglass is given as 16 cubic millimeters per second. We need to find out the time available for a turn. Let's assume that the hourglass is filled with 'x' cubic millimeters of sand.

We can use the formula:

Volume = Rate x Time

Here, the volume of sand is 'x' cubic millimeters, the rate is 16 cubic millimeters per second, and we need to find the time available for a turn, which we can represent as 't' seconds.

So,

x = 16t

We can rearrange this equation to find 't':

t = x/16

This means that the time available for a turn is equal to the volume of sand in the hourglass divided by the rate at which the sand falls.

We don't know the exact volume of sand in the hourglass, but let's assume it's 100 cubic millimeters.

Then,

t = 100/16

t = 6.25 seconds

So, in this case, a player would have approximately 6.25 seconds for their turn before all of the sand falls to the bottom of the hourglass.

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The absolute minimum value of f on the given interval is 8+4π and the absolute maximum value of f on the given interval is 15.

To find the absolute maximum and absolute minimum values of f on the given interval [0,15], we need to first find the critical points of the function and then evaluate the function at those critical points as well as at the endpoints of the interval.

To find the critical points of f, we need to find the values of x where f'(x) = 0 or f'(x) does not exist.

f'(x) = 3x^2 - 1 - 25 = 3x^2 - 26

Setting f'(x) = 0, we get:

3x^2 - 26 = 0

x^2 = 26/3

x = ± √(26/3)

Since √(26/3) is not in the interval [0,15], we only need to consider x = - √(26/3) as a critical point.

Next, we evaluate the function f at the critical point and at the endpoints of the interval:

f(0) = 0(0)^2 - 0 - 25 = -25

f(15) = 15(15)^2 - 15 - 25 = 3375 - 15 - 25 = 3335

f(-√(26/3)) = (-√(26/3))(√(26/3))^2 - (-√(26/3)) - 25

= 26/3 + √(26/3) - 25

To compare these values and find the absolute maximum and minimum, we can use the following observations:

- If the critical point or an endpoint gives the largest value of f, then that is the absolute maximum.
- If the critical point or an endpoint gives the smallest value of f, then that is the absolute minimum.

Comparing the values we found, we can see that:

- The absolute minimum value of f on [0,15] is 26/3 + √(26/3) - 25 ≈ 8 + 4π
- The absolute maximum value of f on [0,15] is 15

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The gradient of the river is approximately 0.3947%, calculated by dividing the change in elevation of 1500 feet by the horizontal distance of 72 miles (converted to 380,160 feet).

The gradient of a river is the change in elevation divided by the horizontal distance.

Given that the change of elevation is 1500ft and the length of the river is 72 miles, we first need to convert the units to a consistent system. Let's convert the length from miles to feet, since the change in elevation is given in feet

72 miles = 72 x 5280 feet

72 miles = 380,160 feet

Now we can calculate the gradient using the formula

gradient = change in elevation / horizontal distance

gradient = 1500 ft / 380,160 ft

Simplifying, we get

gradient = 0.003947

Therefore, the gradient of the river is approximately 0.003947, which can be expressed as a percentage by multiplying by 100

gradient = 0.003947 * 100

gradient = 0.3947%

So, the gradient of the river is approximately 0.3947%.

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The probability of not getting an even number when spinning the spinner once is [tex]\frac{5}{11}[/tex].

You want to know the probability of not getting an even number when spinning a spinner divided into 11 equal sections numbered from 0 to 10.

Step 1: Identify the even numbers in the given range (0 to 10). The even numbers are 0, 2, 4, 6, 8, and 10.

Step 2: Count the number of even numbers. There are 6 even numbers in the given range.

Step 3: Calculate the total number of possible outcomes when spinning the spinner. There are 11 possible outcomes (0 to 10).

Step 4: To find the probability of not getting an even number (P(not even)), subtract the number of even numbers from the total number of outcomes. This will give you the number of odd numbers: 11 - 6 = 5.

Step 5: Now, divide the number of odd numbers by the total number of outcomes to find the probability: P(not even) = 5/11.

So, the probability of not getting an even number when spinning the spinner once is [tex]\frac{5}{11}[/tex].

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The probability that the return of the portfolio will be less than -43.5% in any given year is 0.0139, or approximately 1.39%.

To solve this problem, we need to standardize the value of -43.5% using the given mean and standard deviation.

z = (x - mu) / sigma

where z is the z-score, x is the value we want to find the probability for (-43.5%), mu is the expected return (13.2%), and sigma is the standard deviation (18.9%).

Substituting the given values:

z = (-0.435 - 0.132) / 0.189

z = -2.22

We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.22.

P(Z < -2.22) = 0.0139

Therefore, the probability that the return of the portfolio will be less than -43.5% in any given year is 0.0139, or approximately 1.39%.

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The amount of milk Jonah bring is 8 quarts of milk

From the question, we have the following parameters that can be used in our computation:

Jonah brought 16 pints of milk to share with his soccer teammates at halftime.

This means that

Milk = 16 pints of milk

By the metric units of conversion, we have

1 pint of milk = 0.5 quart of milk

Substitute the known values in the above equation, so, we have the following representation

Milk = 16 quarts of milk * 0.5

Evaluate

Milk = 8 quarts of milk

Hence, the amount of milk is 8 quarts of milk

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The probability of Suzan getting one of each color other than fluorescent pink, given that she gets the fluorescent pink one, is 108/1001 or approximately 0.108.

To find the probability of Suzan getting one of each color other than fluorescent pink, given that she gets the fluorescent pink one, we can use counting techniques.

First, we need to find the total number of ways Suzan can choose four marbles out of the 14 in the bag. This can be calculated using combinations, which is 14 choose 4 or (14!)/(4!10!) = 1001.

Next, we need to find the number of ways Suzan can choose one of each color other than fluorescent pink, given that she already picked the fluorescent pink one. There are three red, three green, three yellow, and four orange marbles left in the bag. Suzan needs to choose one from each color, which can be done in (3x3x3x4) = 108 ways.

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To compute the 99% confidence interval for the population mean, you need to determine the appropriate sample size to ensure that the sample mean does not deviate from the population mean by more than 1.3. The key terms involved in this process are the confidence interval, sample size, population mean, and sample mean.

The confidence interval represents the range within which the population parameter (in this case, the population mean) is likely to fall, given a certain level of confidence. A 99% confidence interval means that you are 99% confident that the true population mean falls within the specified range.

To calculate the required sample size, you will need to use the formula for the margin of error (E), which is E = (Zα/2 * σ) / √n, where Zα/2 is the critical value associated with the desired level of confidence (99%), σ is the population standard deviation, and n is the sample size.

Since you want the sample mean to not deviate from the population mean by more than 1.3, you will need to set E = 1.3 and solve for n. After finding the critical value for a 99% confidence interval (which is approximately 2.576) and assuming you know the population standard deviation, you can plug these values into the formula and solve for n.

By doing this, you will be able to determine the appropriate sample size to ensure that the 99% confidence interval for the population mean is within 1.3 units of the sample mean.

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We can say with 90% confidence that the increase in proportion of people satisfied with their financial situation is between 1.05% and 6.71%.

To calculate the confidence interval for the increase in proportion of people satisfied with their financial situation, we need to first calculate the proportions for both years:

Proportion in year 1 = 478/2038 = 0.2342
Proportion in year 2 = 537/1967 = 0.2730

The increase in proportion is:
0.2730 - 0.2342 = 0.0388

To calculate the confidence interval, we can use the formula:
CI = (point estimate ± (critical value x standard error))

The point estimate is the increase in proportion we just calculated: 0.0388

The critical value can be found using a z-table for a 90% confidence level. The z-value for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:
sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

where p1 and n1 are the proportion and sample size for year 1, and p2 and n2 are the proportion and sample size for year 2.

Plugging in the values, we get:
SE = sqrt[(0.2342(1-0.2342)/2038) + (0.2730(1-0.2730)/1967)] = 0.0174

Now we can plug in all the values to get the confidence interval:
CI = (0.0388 ± (1.645 x 0.0174)) = (0.0105, 0.0671)

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The total number of different choices for the representative is 114

The number of choices for the representative to the university committee is the sum of the number of CS faculty members and the number of CS majors who are not faculty members.

Since no one can be both a faculty member and a student.

The number of choices for a faculty member is simply the number of members of the CS faculty, which is 9.

The number of choices for a CS major who is not a faculty member can be calculated by subtracting the number of CS faculty members from the total number of CS majors: 114 - 9 = 105.

Therefore, the total number of different choices for the representative is:

9 + 105 = 114

So there are 114 different choices for the representative to the university committee.

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Based on the information given in (6), we know that the mean is 65 and the standard deviation is 3. we can use the empirical rule to estimate the probability of the sample mean being within one standard deviation away from the mean in either the positive or negative direction.

According to the empirical rule, approximately 68% of the sample means will fall within one standard deviation away from the mean in either direction. Therefore, the probability of the sample mean being within one standard deviation away from the mean in either the positive or negative direction is approximately 0.68 or 68%.

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Answer:

22/30

33/45

7.33333...

%73.33..

Step-by-step explanation:

to find it in a different form as a fraction you can simply multiply it by any number greater than 1 and just make sure you multiply the numerator and the denominator by the same number

to get a decimal simply divide it

to get a percentage you divide the numbers and multiply that by 10.

The total amount owed by the students for the week is $[tex]$28[/tex].

An amount owed refers to total of the money a person owe us from time to time which can include loan and any unpaid interest, fees and expenses. It can also be an ordinal expenses such as school fee etc.

The total amount owed by the student will be:

= $3.00 + $8.00 + $7.00 + $10.00

= $28

Full question "On the first Monday of each month, the school sends home a note that includes each student's lunch account balance. These students owe money. Student 1 =$3.00, Student 2 - $8.00, Student 3 - $7.00, Student 4 - $10.00. What is the total amount owed by the student?".

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Hence, the margin of error for this 95% confidence interval of a population proportion is 5.4%.

The margin of error for a confidence interval is the distance between the sample statistic (in this case, the sample proportion) and the confidence interval limits. To find the margin of error, we can use the formula:

Margin of error = (upper limit - lower limit) / 2

In this case, the lower limit of the 95% confidence interval is 64.5% and the upper limit is 75.3%. So the margin of error is:

Margin of error = (75.3% - 64.5%) / 2

Margin of error = 10.8% / 2

Margin of error = 5.4%

Therefore, the margin of error for this 95% confidence interval of a population proportion is 5.4%.

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The  absolute maximum value of f(x) on the interval [-3,9] is approximately 1.3 x 10^9 and the absolute minimum value of f(x) on the interval [-3,9] is 0.

To find the absolute maximum and minimum values of the function f(x) = x^8e^(-x) on the interval [-3, 9], we first need to find the critical points and endpoints of the function on the interval.

Taking the derivative of the function, we get:

f'(x) = x^7e^(-x)(8-x)

Setting f'(x) equal to zero, we get critical points at x=0 and x=8. We also need to check the endpoints of the interval, x=-3 and x=9.

Now we need to evaluate the function at these points to find the absolute maximum and minimum values.

f(-3) ≈ 3.3 x 10^5
f(0) = 0
f(8) ≈ 1.3 x 10^9
f(9) ≈ 4.4 x 10^8

Therefore, the absolute maximum value of f(x) on the interval [-3,9] is approximately 1.3 x 10^9 and the absolute minimum value of f(x) on the interval [-3,9] is 0.

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Answer:

-14°C

Step-by-step explanation:

The temperature at 12 noon = 10°C (given)

The temperature decreases by 2°C in 1 hour (given)

Thus, the temperature decreases by 1°C in 1/2 hour

Temperature 10°C above zero - Temperature 8°C below zero = 10 - (- 8) = 10 + 8 = 18°C

The temperature decreases by 18°C in 1/2 × 18 = 9 hours

Thus, from 10°C above zero to 8°C below zero it takes 9 hours

Total time = 12 noon + 9 hours

= 21 hours = 9 pm

Thus, at 9 pm temperature would be 8°C below zero.

(ii) The temperature at 12 noon = 10°C

The temperature decreases by 2°C every hour

The temperature decrease in 12 hours = - 2°C × 12 = - 24°C

At midnight, the temperature will be = 10°C + (-24°C) = -14 °C

Therefore, the temperature at mid night will be 14°C below 0.